Solve for $x$ and $y$ using elimination. ${-5x-y = -16}$ ${-4x+y = -11}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $-9x = -27$ $\dfrac{-9x}{{-9}} = \dfrac{-27}{{-9}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-5x-y = -16}\thinspace$ to find $y$ ${-5}{(3)}{ - y = -16}$ $-15-y = -16$ $-15{+15} - y = -16{+15}$ $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ You can also plug ${x = 3}$ into $\thinspace {-4x+y = -11}\thinspace$ and get the same answer for $y$ : ${-4}{(3)}{ + y = -11}$ ${y = 1}$